As a benchmark, we computed optimal ATSP tours for 1,107 test instances.
The Concorde code ([1]}) solves symmetric instances of the TSP, so we applied a standard transformation of the ATSP to the TSP, splitting each stop into a pair of nodes, one for incoming edges and the other for outgoing edges (see [2]}).
The TSP instances thus obtained were solved with Concorde in an average of 142 seconds of computation time on a single core of a linux workstation, equipped with an Intel Xeon Gold 6238 CPU @ 2.10GHz processor.
This is not an efficient way to solve instances of the ATSP, but it allowed us to easily obtain optimal tours for the test set.
\(\begin{tabular}{cc} \hline Solution Set & Mean Travel Time \\ \hline ATSP Tours & 10853.3s \\Driver Tours & 12250.0s \\ \hline \end{tabular}\) 
